The performance of a kernel HAC estimator depends on the accuracy of the estimation of the normalized curvature, an unknown quantity in the optimal bandwidth represented as the spectral density and its derivative. This paper proposes to estimate it with a general class of kernels. The AMSE of the kernel estimator and the AMSE-optimal bandwidth are derived. It is shown that the optimal bandwidth...

We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on (0,∞). For the maximum likelihood (ML) estimator and least squares (LS) estimator, we state qualitative properties, prove consistency and propose a computational algorithm. For the LS estimator and its derivative, we als...

We look into the problem of estimating a regression function that exhibits peaks, i.e. discontinuities in the first derivative. In the neighbourhood of such a discontinuity we investigate the behaviour of the local linear fit and find that it is not consistent for estimating the first derivative, and for estimating the function itself it loses in the rate of convergence. Indeed, near such point...

This paper addresses a simplified frequency offset estimator for multiple-input–multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems over frequency-selective fading channels. By exploiting the good correlation property of the training sequences, which are constructed from the Chu sequence, carrier frequency offset (CFO) estimation is obtained through factor decomposi...

In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with timevarying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative o...

The derivative patch recovery technique developed by Zienkiewicz and Zhu 1]-3] for the nite element method is analyzed. It is shown that, for one dimensional problems and two dimensional problems using tensor product elements, the patch recovery technique yields superconvergence recovery for the derivatives. Consequently, the error estimator based on the recovered derivative is asymptotically e...

We study the asymptotic distribution of three-step estimators of a …nite dimensional parameter vector where the second step consists of one or more nonparametric regressions on a regressor that is estimated in the …rst step. The …rst step estimator is either parametric or non-parametric. Using Newey’s (1994) path-derivative method we derive the contribution of the …rst step estimator to the in‡...

In this paper, we discuss a unified theory for and performance evaluation of the ridge direction estimation through the minimization of the integral of the second directional derivative of the gray-level intensity function. The primary emphasis of this paper is on the ridge orientation estimation. The subsequent ridge detection can be performed using the traditional methods of using the zero cr...

Masry (1996b) provides estimation bias and variance expression for a general local polynomial kernel estimator in a general multivariate regression framework. Under smoother conditions on the unknown regression and by including more refined approximation terms than that in Masry (1996b), we extend the result of Masry (1996b) to obtain explicit leading bias terms for the whole vector of the loca...

We formulate optical flow estimation as a two-stage regression problem. Based on characteristics of these two regression models and conclusions on modern regression methods, we choose a Least Trimmed Squares followed by weighted Least Squares estimator to solve the optical flow constraint (OFC); and at places where this one-stage robust method fails due to poor derivative quality, we use a Leas...